Question: Simplify the following expression: $ p = \dfrac{-5}{6} - \dfrac{6x - 10}{-6x - 5} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-6x - 5}{-6x - 5}$ $ \dfrac{-5}{6} \times \dfrac{-6x - 5}{-6x - 5} = \dfrac{30x + 25}{-36x - 30} $ Multiply the second expression by $\dfrac{6}{6}$ $ \dfrac{6x - 10}{-6x - 5} \times \dfrac{6}{6} = \dfrac{36x - 60}{-36x - 30} $ Therefore $ p = \dfrac{30x + 25}{-36x - 30} - \dfrac{36x - 60}{-36x - 30} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{30x + 25 - (36x - 60) }{-36x - 30} $ Distribute the negative sign: $p = \dfrac{30x + 25 - 36x + 60}{-36x - 30}$ $p = \dfrac{-6x + 85}{-36x - 30}$ Simplify the expression by dividing the numerator and denominator by -1: $p = \dfrac{6x - 85}{36x + 30}$